According to several recent articles in The Journal of Foreign Affairs, world-wide violence is actually going down and has been for several decades despite appearances to the contrary. So there are some factors that play a role in the likelihood of war beyond just the presence of violent conflict but this does suggest that the possibility has perhaps gone down.

The second major reason for war not being likely, particularly on a major scale, is the incredible connections between various world-wide markets and the fear that any large nation has of upsetting the economic balance over anything that isn't absolutely vital. This helps to decrease the likelihood that a super power is going to go to war anytime soon.

Though countries may battle, it is unlikely that it will spread worldwide because of all of the connections we have. First-world countries, in particular, are involved in a web of alliances that make a worldwide war highly unlikely.

World War III would technically be a European-based war, with Germany and England at odds and other countries allied with them. If a war was started by another country, or other countries were fighting in it, I don't tnink you could techically call it World War III.